The application of OFDM within a multi-user downlink scenario is considered. Thereby, two problems occur. First, due to OFDM, the transmit signal exhibits a large peak-to-average power ratio (PAR). Second, the multi-user interferences have to be equalized (or precoded) at the transmitter side. In this article, we address combined precoding and PAR reduction. As precoding schemes sorted Tomlinson-Harashima precoding (sTHP) and its lattice-reduction-aided variant (LRA-THP) are considered. In order to reduce the PAR, we review the scheme selected sorting (SLS), which is a combined approach of PAR reduction and precoding with sTHP. Based on this idea, the novel PAR reduction scheme selected basis (SLB) is introduced which combines PAR reduction with the precoding approach LRA-THP. It can be shown that SLB achieves very good PAR reduction performance and hardly influences the error performance. Both schemes, SLB and SLS, are compared with simplified selected mapping (sSLM), the only PAR reduction scheme from the SLM family, which can be applied in multi-user downlink scenarios. The comparison is done on the basis that the respective schemes exhibit the same computational complexity. In terms of PAR reduction performance, it turns out that sSLM outperforms SLS, whereas the performance of sSLM and SLB is similar. Noteworthy, the great benefit of SLB or SLS is that no side information has to be communicated to the receiver as it is necessary with sSLM. Moreover, using SLB, full diversity error rate performance is possible with only low-PAR transmit signals.
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